Question

9. Without actually dividing find which of the following are terminating decimals. 3/25, 11/18, 13/20 & 41/42​

Answer 1

Step-by-step explanation:

So 3/25 is terminating. 11/18 is non terminating. 13/20 is terminating. 41/42 is non terminating.

Answer 2

Step-by-step explanation:

$(i). \frac{3}{25} \\ \frac{3}{25} \\ = \frac{3}{5 \times 5} \\ = \frac{3}{ {5}^{2} } \\ = \frac{3}{ {5}^{2} } \times \frac{ {2}^{2} }{ {2}^{2} } \\ = \frac{3 \times 4}{ {10}^{2} } \\ = \frac{12}{100} \\ = 0.12 \\ \: therefore \: \frac{3}{25} \: is \: a \: terminating \: decimal$

$(iv). \frac{41}{42} \\ \frac{41}{42} = \frac{41}{2 \times 3 \times 7} \\ this \: is \: not \: a \: terminating \: decimal \\ because \: this \: is \: not \: in \: the \: form \: of \: {2}^{m} \times {5}^{m} \\ therefore \: \frac{41}{42} \: is \: non \: terminating \: decimal$

$(ii). \frac{11}{18} \\ \frac{11}{18} = \frac{11}{3 \times 3 \times 2} \\ \: this \: is \: not \: a \: terminating \: decimal \: \\ because \: this \: is \: not \: in \: the \: form \: of \: {2}^{m} \times {5}^{m} \\ therefore \: \frac{11}{18} \: is \: non \: terminating \: decimal$

$(iii). \frac{13}{20} \\ \frac{13}{20} = \frac{13}{2 \times 2 \times 5} \\ = \frac{13}{ {2}^{2} \times {5}^{1} } \\ = \frac{13}{ {2}^{2} \times {5}^{1} } \times \frac{ {5}^{1} }{ {5}^{1} } \\ = \frac{13 \times 5}{ {2}^{2} \times {5}^{2} } \\ = \frac{65}{ {10}^{2} } \\ = \frac{65}{100} \\ = 0.65 \\ \: therefore \: \frac{13}{20} \: is \: a \: terminating \: decimal$